I'm a guitarist, so it may just take some time to get used to a larger instrument.

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Not saying Fender Jazz necks are the thinest out there but they are one of the thinnest!!! Their are lighter basses but if you like the sound look for one of the Ash body Jazzes, mine is really light!!! Like you said though, may just need to adjust to a bass in general.

A Fender Geddy Lee will have a thinner neck back to front. As others have mentioned, many of the Ibanez basses might work, specifically the Soundgear line. If you look used, Peavy Foundations or Carvins from the late '80s to early'90s might work for you.